Anonymous
Anonymous asked in Science & MathematicsPhysics · 2 months ago

A cannon fires a cannonball at an angle of 45° with an initial velocity of 75 m/s off a cliff that is 150 m high?

What is the max height that the cannonball reaches?

What is the total time the cannonball is in the air?  

What is the total distance the cannonball travels along the horizontal? 

1 Answer

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  • 2 months ago

    1.

    Take g = 9.8 m/s², and take all upward quantities to be positive.

    Consider the vertical motion (uniform acceleration motion):

    Initial velocity, u = 75 sin45° m/s

    Final speed, v = 0 m/s

    Acceleration, a = -9.8 m/s

    v² = u² + 2as

    0 = (75 sin45°)² + 2(-9.8)s

    s = (75 sin45°)² / [2(9.8)]

    s = 143 m

    Maximum height = (143 + 150) m = 293 m

    ====

    2.

    Consider the vertical motion (uniform acceleration motion):

    Initial velocity, u = 75 sin45° m/s

    Displacement, s = -150 m

    Acceleration, a = -9.8 m/s

    s = ut + (1/2)at²

    -150 = (75 sin45°)t + (1/2)(-9.8)t²

    4.9t² - (75 sin45°)t - 150 = 0

    t = {-(-75 sin45°) + √[(-75 sin45°)² - 4(4.9)(-150)]} / [2(4.9)]

    Time taken, t = 13 s

    ====

    3.

    Horizontal distance = (75 cos45°) (13) = 689 m

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